About

This is an experiment that was created out of curiosity. The purpose is to see how computer generated sequences
take form given certain restrictions. It's inspired by the great
On-Line Encyclopedia of Integer Sequences database but with the intention to be
entirely machine generated.

Helping out

If you have a sequence that is not in the database but should be because it can be machine generated.
I will never add a single sequence, but if you have found an underlying generative form that interesting I will try to
add it.
This will capture multiple sequences on the same form. E.g. when the recursive form it automatically resulted
in large amounts of new sequences.

Contact

If you have any feedback or questions, please don't hesitate to contact me. You can contact me at jon AT jonkagstrom
DOT com or
via twitter

This sequence is probably the reason I built this site. A while back I was playing with the Sieve of Eratosthenes.
By counting how often each term strike out following composite numbers this sequence appeared.
3 strikes out every second, 5 every third, 7 every 3.75, 11 every 4.375 and so on. I had no idea that this was
Euler Zeta with exponent 1 at the time. I asked a friend who is very good at maths to figure out the formula,
and after a while he came back with the answer. Somewhere here I figured that a program should be able to give me
answers, so I don't have to ask my friend all the time :) This formula is closely related to the Riemann hypothesis.
The generated code is a(n)=a(n-1)/(1-1/p(n)), a(0)=2.

Finally a sequence I ran into by chance when I was adding charts to the site. I've no idea what it means or if it has
any value. But it looks pretty funky. (n-a(n-1))/(a(n-2)+a(n-2)), a(0)=1, a(1)=2

Algorithm

The algorithm generates stack machines that are executed with different input (0≤n<N). The output of each execution form
a sequence that is stored. Duplicated sequences are detected, so that different stack machines can generate the same
sequence. The simplest stack machine per function class is chosen. I'm not a mathematician so I have kind of made up
a definition for each function type (constant, n, prime, recursive and prime-recursive). What more types could I add?

Future

I don't know where to take this project, here are some ideas.

Add more operators

Displayed infix in reduced normal form

Better search options

More sequence analysis such as convergence tests

Disclaimer

Most of the code was written on my spare time over with a baby in one arm and my laptop in the
other.
There are at least a few bugs in there. Also I'm aware that some sequence properties may be false. They are derived
from a limited sequence. E.g. it will mark a sequence as monotonic if it appears to be in the first terms.
You should think of it as 'so far monotonic'.

2017-07-21 - Using 50 terms instead of 25 for indexing. Added floor. Use high
precision at top
when opening sequence. Added ~ for approximate searches (each term within 5%) e.g. ~17,20,26,33,41,46,55,66.
Bunch of bug fixes.